A fair, six-sided number cube has the numbers 2, 2, 4, 4, 6, 6 on its faces. Sarah rolls this number cube 10 times and records the number of times a 2 is rolled.Have the conditions for a binomial setting been met for this scenario?

There are a fixed 10 rolls, and each roll is independent of the others. On each roll, success (rolling a 2) has probability 2/6 = 1/3; failure has probability 2/3, so there are two possible outcomes for the recorded event. The probability stays the same on every roll, so all four BINS conditions are met. Repeated numbers on the faces do not make the cube unfair.

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